The cut and fill areas for each station between points A (St. 0+00) and B (18 +0

Question

The cut and fill areas for each station between points A (St. 0+00) and B (18 +00) are given below. Draw the mass diagram using a swell factor of 10%. (Note: 1 + 00 corresponds to a distance of 100 feet from Point A) Station (ft) Point A, 000 1 00 200 3 +40 4+20 5 +00 6+ 50 7+ 10 8+00 9 +00 10+30 11 10 12 00 13 + 20 14+ 70 15 50 16 + 40 17 00 Point B) 1800 Area Cut (sq.ft) Area - Fill (sq.ft) 200 160 110 50 40 45 70 80 120 180 220 180 150 100 80 30 40 60 80 60 80 90 100 190 210 170 120 70 50 70 40 50 40 70 100 150 210 180

Explanation / Answer

To calculate Ordinate of Mass Diagram , we will evaluate the total net volume of material excavated or filled between any two given stations.

Between any given two stations( 1&2) , volumne of fill/cut can be calculated as:

Vcut(in yd3) = L (A1cut + A2cut)/54

Vfill (in yd3)=   L (A1fill + A2fill)/54

In this case L is constant= 100 ft.

For swell factor , Volume of fill is decreased by 10%, therefore, V(adjusted fill)= Vfill/1.1

Now take a example for station 0 and 1:

Vcut=(200+160)*100/54=666.67 yd3

Vfill=(60+80)*100/54=259.259 yd3

Vadjusted fill= Vfill/1.1=235.69 yd3

Mass ordinated=Vcut-Vadjusted fill=666.67-235.69=430.97 yd3

Similarly calculating for all stations:

Now plotting this on graph with net cumulative volume on Y axis and station at X-axis:

Station End Area(Sq. ft) Cut Fill 0 200 60 1 160 80

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